Thin, planar illumination systems are desirable for many applications such as, for example, low-profile back-illuminated displays. FIG. 1 illustrates such an illumination system 100 fabricated by coupling a discrete light source, e.g., a light-emitting diode (“LED”) 102 to a narrow face 104 of a waveguide 106. Generally, a waveguide 106 having a refractive index of N=1.5 and an LED 102 having Lambertian output characteristics, combined as in the illumination system 100, have a theoretical maximum coupling efficiency limit of 85%. That is, at most 85% of the light emitted by the LED 102 will be trapped within the waveguide 106, and the remaining portion of the emitted light will be lost.
This coupling inefficiency may be attributed to the constraints inherent in the side-emitting LED design of the illumination system 100. While thinner waveguides are desirable, the thickness t of the waveguide must be larger than the width d of the LED in order to achieve coupling efficiencies approaching 85%. Relatively high coupling efficiencies (e.g., greater than approximately 70%) are difficult to obtain for cases where the thickness t of the waveguide is smaller than the width d of the LED. Thus, as waveguides become thinner, the coupling efficiency of the waveguide decreases and more light is lost. The coupling inefficiency may even set a practical lower bound on the thickness of the waveguide 106. In addition, many side-emitting illumination systems utilize specially engineered LED and waveguide structures in order to increase the coupling efficiency. These structures not only add to the complexity and cost of the illumination system 100 but also increase its thickness.
Therefore, there is a need for systems and methods of coupling LEDs to waveguides in which (i) coupling efficiencies greater than approximately 85% are obtained for t≈d, and (ii) high coupling efficiencies greater than approximately 70% are obtained for t<d.